Article ID Journal Published Year Pages File Type
6420156 Applied Mathematics and Computation 2015 15 Pages PDF
Abstract

This paper presents a nonlinear image interpolation algorithm. The suggested method is based on the moving least squares (MLS) projection technique, but introduces a fundamental modification. The algebraic polynomial-based MLS methods provide very satisfactory results. However, the associated approximation space is shift-and-scale invariant so that it cannot be adjusted according to the characteristic of a given data. As a result, when upsampling images, it has a limitation in producing sharp edges such that edges are often blurred in the magnified images. To recover sharper edges, we need to reduce smoothing parameter or adapt a new parameter sharpening the edges. Motivated by this observations, we propose a novel MLS method governed by a set of exponential polynomials with tension parameters such that they can be tuned to the characteristic of given data. Moreover, for a better match to the local structures around the edges, the suggested algorithm uses weights which consider the edge orientation. Numerical results are presented and compared, visually and by using some quantitative fidelity measures (PSNR, EPSNR, SSIM and FSIM), to the bicubic spline interpolation and other recently developed nonlinear methods. The results demonstrate the new algorithm's ability to magnify an image while preserving edge features.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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